Question

Videos are posted on a social media site at an average rate of 0.43 per second.

a) What is the probability that 3 videos are posted in a 2 second time period?

b) What is the expected time until the next video is posted?

c) What is the probability the time until the next video will be more than 1 second but less than 2 seconds?

Answer 1

uploads/sec = 0.43 per sec

a.

P(x videos in t sec) = e^(-0.43*t) * (0.43*t)^x / (x!)

P(3 videos in 2 sec) = e^(-0.43*2) * (0.43*2)^3 / (3!) = 0.0449

b.

E(time) = 1 / avg. rate

= 1 / 0.43

= 2.3256

c.

events/time = uploads / sec = 0.43

P(1<T<2) = P(T>1) - P(T>2)

= e^(-0.43*1) - e^(-0.43*2)

= 0.2273

(please UPVOTE)